Question

A block of wood is floating on water at $0^{0}C$ with a certain volume V above water level. The temperature of water is slowly raised from $0^{\circ }C$ to ${20}^{\circ }C$.How will the volume V changes with the rise of temperature

• A. V will remain unchanged
• B. V will go decreasing from beginning to the end
• C. V will decrease till the temperature of water reaches $4^{\circ }C$ and then it will go on increasing
• D. V will increase till the temperature of water reaches $4^{\circ }C$ and then it will go on decreasing

Answer 1

The correct option is D V will increase till the temperature of water reaches $4^{\circ }C$ and then it will go on decreasing

Let the total volume of the wooden block be $V_0$.

Then the volume of water displaced by block at any given temperature=$V_0-V$

The block remains in equilibrium at all temperatures.

Thus Weigh of block=$mg=(V_0-V){\rho }_{w}g$

$⟹V=V_0-\frac{mg}{{\rho }_{w}g}$

where ${\rho }_w$ is the density of water.

We know that density of water is maximum at $4^{\circ }C$.
Thus the value of $V$ is maximum at $4^{\circ }C.$